A matlab prog which produces 20 steps for the intuitive ...
A matlab prog which produces 20 steps for N-R iteration :
format long;
x=1.8
for i=1:20
i;
x=x-((x-2*sin(x))/(1-2*cos(x))) ;
fprintf('x%d = %.17g\n',i,x)
end
results: ( starting x0=1.8)
x =
1.80000000000000
x1 = 1.9015503550073825
x2 = 1.8955153109517944
x3 = 1.8954942672901975
x4 = 1.8954942670339809
x5 = 1.8954942670339809
x6 = 1.8954942670339809
x7 = 1.8954942670339809
x8 = 1.8954942670339809
x9 = 1.8954942670339809
x10 = 1.8954942670339809
x11 = 1.8954942670339809
x12 = 1.8954942670339809
x13 = 1.8954942670339809
x14 = 1.8954942670339809
x15 = 1.8954942670339809
x16 = 1.8954942670339809
x17 = 1.8954942670339809
x18 = 1.8954942670339809
x19 = 1.8954942670339809
x20 = 1.8954942670339809
we can see the convergence through the digits after the dot , which are not variable .
The best guess for x is x20 = 1.8954942670339809
We also can see the digits after the dot are invariable after the 4th step!
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